Approximate maximum likelihood delay estimation via orthogonal wavelet transform

A novel approximate maximum likelihood algorithm is proposed for estimating the time difference of arrival between signals received at two spatially separated sensors. Prior to cross correlation, one of the channel outputs is optimally weighted at different frequency bands with the use of an orthogonal wavelet transform. It composes an array of multirate filters and is a time-domain implementation of the generalized cross correlation method. However, it does not suffer from the performance degradation due to the errors inherent in spectral estimation obtained from finite length data and is computationally efficient. A simple decision rule is also provided to automatically determine the requisite levels of wavelet decomposition. The effectiveness of the method is demonstrated by comparing, with the direct cross correlator, the Eckart processor and the Cramér-Rao lower bound (CRLB) for different noise conditions and wavelet filter lengths.